Question

an architect wants to draw a rectangle with a diagonal of 25 inches. the length of the rectangle is to be 10 inches more than twice the width. what dimensions should she make the rectangle?

answer
length = inches
width = inches

Explanation:

Define variables and expressions

Let \(w\) represent the width of the rectangle in inches.
The length is \(10\) inches more than twice the width:

$$l = 2w + 10$$

The diagonal of the rectangle is \(25\) inches.

Set up the equation

Using the Pythagorean Theorem Applications knowledge point

$$ w^2 + l^2 = d^2 $$

$$ w^2 + (2w + 10)^2 = 25^2 $$

Expand and simplify the quadratic equation

Using the Solving Quadratic Equations and Quadratic Word Problems knowledge points

$$
LATEXBLOCK0
$$

Solve the quadratic equation

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK1
$$

Since width must be positive, we choose \(w = 7\).

Calculate the dimensions

Using the Quadratic Word Problems knowledge point

$$
LATEXBLOCK2
$$

Answer:

An architect wants to draw a rectangle with a diagonal of 25 inches. The length of the rectangle is to be 10 inches more than twice the width. What dimensions should she make the rectangle?

Length = <blank>24</blank> inches

Width = <blank>7</blank> inches